Problem: $\dfrac{ -2l - 10m }{ -8 } = \dfrac{ -8l - 6n }{ 3 }$ Solve for $l$.
Answer: Multiply both sides by the left denominator. $\dfrac{ -2l - 10m }{ -{8} } = \dfrac{ -8l - 6n }{ 3 }$ $-{8} \cdot \dfrac{ -2l - 10m }{ -{8} } = -{8} \cdot \dfrac{ -8l - 6n }{ 3 }$ $-2l - 10m = -{8} \cdot \dfrac { -8l - 6n }{ 3 }$ Multiply both sides by the right denominator. $-2l - 10m = -8 \cdot \dfrac{ -8l - 6n }{ {3} }$ ${3} \cdot \left( -2l - 10m \right) = {3} \cdot -8 \cdot \dfrac{ -8l - 6n }{ {3} }$ ${3} \cdot \left( -2l - 10m \right) = -8 \cdot \left( -8l - 6n \right)$ Distribute both sides ${3} \cdot \left( -2l - 10m \right) = -{8} \cdot \left( -8l - 6n \right)$ $-{6}l - {30}m = {64}l + {48}n$ Combine $l$ terms on the left. $-{6l} - 30m = {64l} + 48n$ $-{70l} - 30m = 48n$ Move the $m$ term to the right. $-70l - {30m} = 48n$ $-70l = 48n + {30m}$ Isolate $l$ by dividing both sides by its coefficient. $-{70}l = 48n + 30m$ $l = \dfrac{ 48n + 30m }{ -{70} }$ All of these terms are divisible by $2$ Divide by the common factor and swap signs so the denominator isn't negative. $l = \dfrac{ -{24}n - {15}m }{ {35} }$